The PMSU Spectroscopic Survey of Nearby M dwarfs

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PMSU 3

Nearby Star Surveys

1. Introduction

There are two basic arguments which justify finding nearby stars: detailed
study of individual stars, and stellar statistics.
1. Individually, the nearest
stars (of a particular class) are the brightest stars, and therefore permit the
most intense scrutiny of physical characteristics, and star-to-star
variations in those characteristics. We note in passing that the fact that
there are differences to investigate became clear with the completion of the first
successful measurements of stellar parallax: while the two components in Alpha Centauri are
similar in brightness to the Sun (Henderson's parallax, 1839), Bessel's 1838 measurements for 61 Cygni
showed that the fainter star in that pair is ~35 times fainter than the Sun, while Vega
(parallax by Struve, 1841) is brighter by almost the same factor.
2. Statistically,
the scientific justification for compiling a catalogue of the nearest stars is summarised
succinctly by Kuiper (1942): apart from illuminating
details of stellar evolution through their distribution in
the Hertzsprung-Russell diagram, the nearest stars provide the basis for the determination of the stellar
luminosity function, the mass-luminosity relation, the stellar contribution to the local mass density,
the velocity distribution and the stellar multiplicity statistics. Add information on chemical
abundance, and the nearby stars map out the metallicity distribution of the (local) Galactic disk, while
age estimates make these stars
probes of the local star formation history, and the variation of stellar kinematics
(and other parameters) as a function of time.

To provide useful conclusions, statistical studies should be based on an underlying
dataset which provides an unbiased, representative sample of the parent sample, in this
case, stars in the Solar Neighbourhood.
One of the most effective means of satisfying this criterion is to
identify a complete, volume-limited sample of stars: that is, a set of stars defined solely by where
they are in the Galaxy, not by any characteristic (velocity, abundance, luminosity) peculiar
to the stars themselves. There are still inherent difficulties in taking results derived from
analysis of that sample and extending those conlusions to the global Galactic stellar populations:
high velocity stars, particularly members of the halo (Population II), spend relatively little
time near the mid-plane of the disk, and are correspondingly under-represented in a local sample;
similarly, the Sun lies over 100 parsecs from the nearest active star-forming region, and
very young objects are correspondly lacking in the Solar Neighbourhood. However, if those
biases can be characterised to at least some extent, then
the net effects can be taken into account in subsequent analysis.

The nearest stars - the 5 parsec sample: In this type of analysis, the trick is
defining a volume-limited sample which, if not complete, is at least incomplete
in a well understood manner. A first step is to limit the sample to stars on the Sun's doorstep -
set a distance limit of only a few parsecs.
One of the first essays in this regard was by Hertzsprung (1922), who
produced a list of 29 stars with measured parallaxes exceeding 0.2 arcseconds, placing them within
5 parsecs of the Sun. The 5 parsec limit became somewhat of a fiducial marker for the nearby star
census. Hertzsprung's original catalogue corresponds to a star density of 0.055 stars/pc3,
counting separately individual stars in multiple systems. van Maanen (1933) extended the sample
to 39 stars (0.074 stars/pc3), but the sample had shrunk to 34 stars when van de Kamp
took over the book-keeping (van de Kamp, 1940). van de Kamp's sample increased to 39 stars in
1945 and 42 stars in 1953.

Over the next decade, van de Kamp extended the distance limit to 5.2 parsecs, or 17 light
years, and by the 1960s, the sample included 59 stars in 44 systems.
These comprised 31 single stars (including the Sun), 11 binaries and two triple systems (van de Kamp, 1969).
Since the 60s, the accretion rate has decreased: van de Kamp & Lippincott (1975) list 60 stars within
5.2 parsecs in their review article; the present total, including both new discoveries and the more accurate
distances provided by the Hipparcos satellite, has reached 69 stars, but in only 40 systems. Setting the
limit at 5 parsecs, the total is 63 stars in 37 stellar systems (including the Sun). Of these, the
most recent additions are LHS 1565 (Henry et al, 1996), LP944-20 (Tinney, 1998) and
LHS 2090 (Scholz et al, 2001). The first and last are mid-type
M dwarfs (M5.5 and M6.5, respectively), and lie at distances of only ~4 parsecs; LP 944-20 is
spectral type M9, lies at a distance of 4.97 parsecs and is a confirmed brown dwarf; together,
these recent discoveries provide a clear hint that
the goal of completeness may yet to be attained in surveying even the nearest `stars'.
The current census corresponds to a star density of 0.12 stars/pc3, more than double the density
derived by Hertzspring.

The 8 parsec sample: A distance limit of 5 parsecs offers advantages and disadvantages: the main
advantage is high probability of detection; the primary disadvantage is small sample size. Given the
advances in technology made in the last decades of the twentieth century, with the availability of
all-sky surveys at wavelengths from X-ray through optical and near-infrared to radio, it has become
possible to consider extending the scope of the nearest-star census. A distance limit of 8 parsecs
marks a reasonable second step since the increase corresponds to quadrupling the survey volume over
a 5-parsec sample. However, with that increase in distance goes a reduction in areal coverage:
in brief, the southernmost stars have been surveyed less thoroughly for companions, and statistical
analyses are therefore best confined to stars accessible from northern hemisphere observatories. The
following table outlines the salient statistics for the current (23/6/2001) 5-parsec and 8-parsec
sample, comparing the relative numbers of systems and individual stars north and south of decline -30o.
The relative areal coverage is 3:1, with the "northern" (dec > -30o) sample covering 3-pi steradians; thus
the ratios N(south)/N(north) should be close to 0.333

Table P1: North/south statistics

Stars

Systems

Ratio:stars

Ratio:systems

5 parsecs

North

47

33

South

15

13

0.32+/-0.08

0.39+/-0.10

8 parsecs

North

150

104

South

38

32

0.25+/-0.04

0.31+/-0.05

8 vs 5

North

0.31+/-0.05

0.32+/-0.05

South

0.39+/-0.10

0.41+/-0.11

As the Table shows, the 5-parsec sample meets expectations. Indeed, even the 8-parsec sample has a relative number of
northern and southern systems close to the expected 3:1 ratio; however, the southern 8-parsec
sample is clearly lacking in resolved companions.

A major factor in the incompleteness of the companion-star census at southern declinations is
accessibility: the overwhelming majority of the Earth's landmass is north of the equator, and, as a result,
so are the majority of the astronomical observatories. In particular, both Palomar Observatory, the
site of the 48-inch Schmidt and Luyten's wide-field proper motion surveys, and Steward Observatory,
site of Henry's (1991) speckle imaging survey of nearby stars, lie at latitude +33o. With the
current emphasis on high-resolution adaptive optics, and the presence of active observatories
in Chile (ESO, CTIO, Las Campanas), Australia (AAT) and South Africa (SAAO/yyy), this borealic bias
should be remedied in the near future, partly as a result of programs initiated under the NStars aegeis;
however, for the present,a line drawn at -30o declination is the most expedient approach.

The data listed in Table P1 can be used to derive a second statistic: we noted above that the volume
embraced by an 8-parsec sample is approximately four times that of a 5-parsec survey (2144.6 vs 523.5 pc3).
In that case, one would expect a factor of four increase in the number of stars/systems as rlim is
increased from 5 to 8 parsecs; in fact, as Table P1 shows, the ratios are closer to 3:1. Does this represent
residual incompleteness in the 8 parsec sample or a local overdensity in the 5 parsec sample? Henry et al (1994) favour
the former interpretation; we tend to suspect the latter.
Our analysis is given at this site , where we present
data for our sample of stars (and brown dwarfs) within 8 parsecs of the Sun.

Further out and further up - not-quite-so-near stars: An alternative approach to increasing the statistical
significance of nearby star studies is to set a larger distance limit for the sample as a whole, but vary that
limit as a function of absolute magnitude of the individual stars in subsequent analysis. Kuiper (1942) was probably the
first to adopt this approach, implicitly if not explicitly; moreover, his is the first sample to include
a substantial number of stars with distances derived from spectroscopic parallaxes. [One might note that the
luminosity function derived from the latter sample presages the over-abundance of M dwarfs which typfied
similar analyses in the 1960s.]
Kuiper's sample includes 254 stars with estimated or measured parallaxes in excess of 0.095 arcseconds.

Probably the prime exponent of this approach to constructing a local census was Wilhelm Gliese.
His first compilation catalogue included basic data (astrometry, photometry and
spectral types) and inferred parameters (luminosity, kinematics) for 1094 stars in 915 systems
with trigonometric, photometric or spectroscopic parallaxes greater than 49 milliarcseconds, or
distances of up to 20 parsecs from the Sun (Gliese, 1957: CNS1).
These are the original Gliese stars, ordered in Right Ascension (equinox 1950) and designated
Gl 1, Gl 2 ... Gl 915.

Extending the distance limit to 22 parsecs (parallaxes exceeding 44 mas), Gliese increased
the sample size to 1890 stars in 1529
systems, and data for those stars were published in 1969 as the Catalogue of Nearby Stars (Gliese, 1969: CNS2).
These stars were again catalogued in RA order, with the addtions designated as Gl nnn.1, Gl nnn.2 etc: that is,
Gl 268.1 lies between Gl 268 and Gl 269 in RA; Gl 268.2 is east of Gl 268.1, but still west of Gl 269, etc.
That publication prompted the then director of the Royal Greenwich Observatory
and Astronomer Royal, R. v.d.r. Woolley, to tackle this issue, and RGO published its version of a
nearby star census (to r=25 pc) the following year (Woolley, 1970). Subsequent observations have shown
that many of the
RGO stars (designated Wo nnnn) are well outwith the nominal 25 parsec limit.

In the years following the publication of the CNS2, surveys probed to greater depth, and follow-up
observations, particularly of stars from Luyten's proper motion catalogues, revealed more candidates
for the immediate Solar Neighbourhood.
A decade after the completion of the CNS2, Gliese & Jahreiss (1979) published a supplement, including
data for a further 462 stars: 294 had formal parallaxes exceeding 44 mas, and were identified as
GJ 1nnn; a further 159 had incomplete data, but were likely to be within the 22 parsec distance limit,
and were designated GJ 2nnn. The catalogue also included dat for nine new companions of previously-catalogued
stars, and new data for 377 Gliese stars.

Data continued to accumulate during the 80s, and Gliese and
Jahreiss continued to compile those results, producing an electronic version of a third version
of the catalogue in the early 90s (Jahreiss & Gliese, 1991, pCNS3). The distance limit
for that catalogue was extended from 22 to 25 parsecs, i.e. parallaxes > 39 milliarcseconds. As with
the CNS1 and CNS2, distances are derived using trigonometric, photometric and spectroscopic
techniques. However, the separate estimates were not averaged, as had been the case in CNS1 and CNS2:
if the formal relative error in the trigonometric parallax was less than 14%, that value
was adopted; spectroscopic and/or photometric estimates were adopted for stars with low accuracy
astrometry. There are 3803 entries, including data for 3845 components of xxxx systems.
This catalogue was never
published officially, but has served as a reference for several large-scale projects, notably our PMSU
survey, described further below. Jahreiss is currently working on the CNS4, incorporating new
data, notably high accuracy astrometry from the Hipparcos satellite, together with the results of
follow-up observations of the new infrared surveys (eg Delfosse et al, 1998; Scholz et al, 2001).

The Palomar/Michigan State University (PMSU) Survey

The nearby-star samples presented in the CNS1, CNS2 (and supplement) and pCNS3 are
compilations, drawn from the astronomical literature. Each star in those catalogues has a particular
characteristic which indicates a parallax (astrometric, photometric or spectroscopic) exceeding 40 milliarcseconds,
and therefore a distance of less than 25 parsecs. However, data for individual stars and stellar systems
are drawn from a wide range of sources, and span a wide range of quality; moreover, the different techniques
used to estimate distances have themselves a variety of associated uncertainties. The situation is
particularly acute at low luminosities, where many of the pCNS3 nearby-star candidates lacked even a spectral
type estimate.

Given these circumstances, we embarked on a spectroscopic survey of the ~2400 stars in the pCNS3 which
had nominal absolute magnitude estimates of MV > 7.5, and were not classed explicitly
as degenerate white dwarfs. Our choice of spectroscopic rather than photometric observations was driven
partly by pragmatism (quantitative spectroscopy is possible over a wider variety of
conditions than quantitative photometry, while direct astrometry for so many targets imposes a
prohibitive cost in telescope time), but also by the wider possibilities for
probing stellar physics afforded by that technique.
Spectroscopic bandstrength indices can not only provide quantitative estimates of effective
temperature and luminosity, but also probe chemical abundance and chromospheric activity. These
measurements provide a homogeneous set of distance estimates for late-type stars, permitting
a self-consistent appraisal of membership the nearby star sample.
The main observational results from our
survey are presented in two papers - Reid, Hawley & Gizis (1995) and Hawley, Gizis & Reid (1996).

Figure P.1: Definition of the narrowband indices used to measure
TiO, CaH and CaOH bandstrength in the PMSU survey

Our primary method of calibration uses narrowband spectroscopic indices, designed to measure
the depth of the strong molecular absorption bands due to titanium oxide (TiO0, calcium hydride (CaH0
and calcium hydroxide (CaOH). Bandstrengths are determined by measuring the ratio between the
flux within a small wavelength region centred on the feature in question, and a
nearby pseudo-continuum point.
These are essentially narrowband colour indices, but with the advantage that data are taken simultaneously
at all wavelengths; thus, we only require accurate relative flux calibration, rather than
the absolute calibration (and hence photometric conditions) demanded for conventional photometry.
We chose to concentrate on the 6000 to 7500 Angstrom region of the spectrum, a region which
encompasses several TiO features, notably the strong 7050 A bandhead, besides CaH and CaOH.
Figure P.1 illustrates the techniques, and the following table gives the wavelength regions
chosen for in-band and continuum points.

Table P2: Narrowband indices

Index

S1

W

S2

TiO 1

6703-6708

6718-6723

.

TiO 2

7043-7046

7058-7061

.

TiO 3

7079-7084

7092-7097

.

TiO 4

7115-7120

7130-7135

.

TiO 5

7042-7046

7126-7135

.

CaH 1

6345-6355

6380-6390

6410-6420

CaH 2

7042-7046

6814-6846

.

CaH 3

7042-7046

6960-6990

.

CaOH

6345-6354

6230-6240

.

Figure P.2: The correlation between TiO5 bandstrength and spectral
type for M dwarfs. Note the reversal at ~M6.5.

The TiO5 index is particularly useful for calibration purposes. Figure P.2 plots the relation
between TiO5 and spectral type, calibrated using standard stars where the spectral type has been
derived from inspection of the full spectrum (mainly stars from Kirkpatrick et al, 1991).
Note that the TiO5 index reaches maximum strength at a spectral type of ~M6.5, becoming weaker at later
spectral types. This reflects both saturation in the TiO band and the growing strength of
additional absorption, mainly due to vanadium oxide, within the pseudo-continuum band. Formally,
this means that TiO5 is double-valued with spectral type; other features in the spectrum,
notably VO absorption, allow segregation of stars earlier or later than spectral type M6.

Spectral type is correlated primarily with effective temperature. The strong
correlation evident in Figure P.2, between TiO5 and overall type,
emphasises how features vary together, in lock-step, with decreasing temperature -
if all other parameters are approximately equal. All parameters, however, are not always equal; in
particular, changes in chemical abundance can change significantly the emergent spectrum, at almost
all temperatures. In the case of cool M dwarfs, the most striking effect is a change in the
relative strength of the TiO and metal hydride bandstrengths; in part this reflects the fact that
TiO is a double metal, hence doubly sensitive to decreasing metallicity; in part, it reflects the
overwhelming presence of H, which locks up much of the available oxygen in water. The net result
is that K-type metal-poor dwarfs retain strong features of MgH (near 5200 Angstroms), while
later-type M subdwarfs have correspondingly strong CaH features (as illustrated in Figure P.1).
The variations in the strength of these features has been quantified by Gizis (1997), and is
illustrated in Figure P.3. Gizis separates the metal-poor M dwarfs into two sub-types: intermediate
subdwarfs, sdM, which are likely to have an average abundance of [M/H]~-1, and extreme subdwarfs,
esdM, which probably have a mean abundance closer to [M/H]=-2. The overwhelming majority of
stars in the Solar Neighbourhood, and in the pCNS3, are disk dwarfs.

Figure P.4: MV as a function of TiO5 and
CaH2 bandstrength. Magenta crosses mark disk dwarfs from the 8-parsec sample; cyan stars are sdM subdwarfs;
green circles are esdM subdwarfs. Note that subdwarfs are significantly closer to the disk main sequence
in the latter diagram, showing that CaH2 is less susceptible to abundance variations and a better
absolute magnitude estimator

Since the bandstrengths are primarily temperature dependent, they offer the prospect of
photometric parallax estimation, just as with conventional broadband colours. Indeed, as Figure
P.4 shows, the hydride bands are more effective than conventional colours (save, perhaps, (R-I)),
in being almost independent of metallicity. These calibrations therefore offer the possibility
of estimating distances to all of the M dwarfs in the pCNS3.

PMSU observations

The starting point for our survey was the sample of 2227 stars from the pCNS3 which
were either listed explicitly as M dwarfs (spectral type M0 or later, or simply m), or
which were identified as having absolute magnitudes MV > +8.0 and were
not listed as white dwarfs. Of these stars, 1876 lie north of declination -30o,
and those stars were discussed in Paper I (Reid et al, 1995 - PMSU1); the remaining 351 were
included in PMSU2 (Hawley et al, 1996). Most of the observations for PMSU1 were made using the
Palomar 60-inch telescope, supplemented by the 200-inch and Keck for the faintest
stars, while the southern stars were observed from CTIO. Our spectra show that 61 of the PMSU1 stars
and 30 PMSU2 stars are misclassified early-type stars, white dwarfs or M giants.
We were unable to obtain data for 130 stars listed in PMSU1,
since those stars are close companions of much brighter stars; the same holds for only a dozen stars
in PMSU2. The relatively smaller number in the latter sample is more likely due to incompleteness in
companion searches in the south than to a real deficit of companions. That incompleteness, and
the absence of a deep proper motion survey similar to Luyten's work from Palomar, led us to
restrict the main statistical analysis to the "northern" (or at least "accessible from the northern
hemisphere") sample included in PMSU1. Some of those results are summarised here,

Figure P.5: Comparison between distance estimates in pCNS3
and subsequent measurements based on Hipparcos parallax data. the lower panel shows that there is no
systematic offset as a function of MV

Before embarking on that summary, we briefly consider the impact of new data.
Since the completion of our survey, new observations have become available for many stars,
notably the astrometric results from the Hipparcos survey, while high spatial-resolution
adaptive optics work and high spectral resolution radial velocity surveys have turned up many
new companions to known nearby stars. The main result of the Hipparcos observationss has been
to identify a significant number of pCNS3 stars with parallaxes of less than 39 mas, removing
those stars from the 25-parsec sample. Figure P.5 compares pre- and post-Hipparcos distance
estimates for pCNS3 stars. This result is not unexpected, since volume sampling effects
will tend to produce this kind of bias in parallax measurements: since there are more
stars with pi < pi0 than pi > pi0, symmetric errors will scatter a larger
number of distant stars into a sample than nearby stars out of a sample.
On the other hand, Hipparcos
only added a small number of stars to the nearby sample, at least partly because the
mission involved a pointed survey: Hipparcos targeted specific objects, becoming incomplete
for stars fainter than V~8 (the limit is galactic latitude dependent) and observing very few
stars fainter than V=12 (and none fainter than V=13). Thus, while Hipparcos
could target all stars suspected a priori of being within 25 parsecs, it provides only
inomplete coverage of stars not suspected of being within 25 parsecs, but which
actually are. Thus, care is required in selecting a statistical sample for analysis.

Finally, more accurate radial velocities are now available for many stars - notably from
Delfosse et al (1998) and from the P60 echelle data included in PMSU3 (Gizis et al, 2002).
Those data, together with the revised distances, lead to revised estimates of space motions
for several hundred stars.

We have incorporated all of these new measurements in revised versions of the relevant
data tables from PMSU1 and PMSU2. Those tables are available at the bottom of this page, both
as ascii files and in html format.

Results from PMSU

Figure P.6: The distance distribution of the 1684
stars in the northern sample.

Our survey includes observations of 1684 confirmed M dwarfs north of decline -30o.
Those stars include apparently-single M dwarfs, M dwarf companions of earlier-type stars and
M dwarf binary, triple and quadruple systems.
Figure P.6 plots the distance distribution as a function of absolute magnitude, making no distinction
amongst these categories. Clearly, the sample becomes increasingly less complete with increasing
distance at fainter absolute magnitudes. That bias needs to be taken into account before
attempting statistical analysis of the sample.

Figure P.7: The run of system density with distance: these
data are computed from the M-dwarf system sample, including only single M dwarfs and systems
with M dwarf primary stars. The absolute magnitude refers to the brightest star in the
system. The vertical line marks the distance chosen to represent the completeness
limit. Note that there are only 4 systems in the MV=15.5 `complete' sample.

One method of setting compelteness limits is to look at the run of density with increasing
distances as a function of absolute magnitude: we expect initial fluctuations, a flattening, and then
a downturn as the sample becomes incomplete. Figure P.7 plots those data for the PMSU sample,
where the densities are the number of systems per unit volume, grouped by the
absolute magnitude of the brightest star in the system. The vertical lines mark the location of
our adopted completeness limits. Those values are identical to the PMSU limits except for MV=9.5,
where we have reduced the limit from 20 to 18 parsecs. The statistics are as follows:

Table P3: The luminosity function for the PMSU sample

MV

dlim (pc)

Nsys

density

Nstars

density

N Hip

8.5

22

103

0.0031

123

0.0037

6

9.5

18

92

0.0050

102

0.0056

3

10.5

14

64

0.0074

79

0.0092

-

11.5

14

66

0.0077

84

0.0097

3

12.5

14

71

0.0083

92

0.0106

1

13.5

10

23

0.0073

31

0.0099

-

14.5

10

13

0.0041

16

0.0051

-

15.5

5

4

0.0101

9

0.0229

-

16.5

5

1

0.0025

3

0.0077

-

17.5

5

2

0.0051

3

0.0077

-

We adopt the same distance limits for companion stars as primaries, although in
principle the former might be expected to have more distant completeness limits, dependent
more on the absolute magnitude of the primary.
Note the sharp drop in the density profile for MV=15: the high local density
is contributed by 4 systems. It is possible that the appropriate completeness
limits is actually 8-9 parsecs (see our 8-parsec sample discussion).
We also list the number of Hipparcos stars which fall within these distance limits but were not
included in the pCNS3 (see Table 1D, PMSU2).

We have recently combined the revised PMSU sample with an Hipparcos-defined sample of
stars with d < 25 parsecs and MV < 8.0, and used those data to determine the
nearby-star luminosity function for -1 < MV < 18, the present-day mass function
and the initial mass function. See this page for a full discussion.

Given a volume complete sample, we can determine systemic and stellar (star-by-star) volume
densities, and those data are listed in the table. The resultant luminosity function is plotted
in Figure P.8, and compared with data from photometric surveys (i.e. deep, moderately wide-field
starcounts, using photometric parallaxes to estimate distances), and against Wielen's (1974)
original analysis of the CNS2. The results are entirely compatible with our analysis from
PMSU1: a broad maximum near MV=12.5, but not as pronounced as in the photometric
studies. The overall densities are lower than those derived by Wielen (and note the large
uncertainties in that analysis). The reasons for the difference with respect to the
photometric analyses are discussed by Reid & Gizis (1997), and most likely stem from Malmquist
effects introduced by the sharp jump in the (MV, (V-I)) diagram at (V-I)~3; the
lower densities compare to Wielen reflect the gradual reduction of the sample as stars
with over-estimated parallaxes are removed.

Figure P.9: Stellar kinematics for the complete system sample

These data also permit investigation of the statistics of stellar motions, the local stellar
kinematics. The (V, U) and (V, W) velocity distributions for the complete system samples are
plotted in figure P.9, where U is the velocity towards the Galactic centre, V the velocity in the direction
of rotation and W the velocity towards the North Galactic Pole.

The PMSU catalogues

The PMSU catalogues - these have been updated to include new distance measurements, notably
from Hipparcos, newly discovered companions, and more precise radial velocity data. The derived
parameters (MV, (U, V, W) space motions) have been re-computed using the new data.
We have also corrected the original published tables for
known errors in positions, magnitudes and spectral types.